Finite Group Databasebeta

← C3×#83691 #11896287

Subgroups — C3×#83691 #11896287

Order 1152.

788 conjugacy classes of subgroups.

The subgroup lattice has 727 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2C3×#5585C211yesmaximal, characteristic
3C3×#5089C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5C3×#5068C211yesmaximal, characteristic, complemented
6C3×#5067C211yesmaximal, characteristic
7C3×#5066C211yesmaximal, characteristic, complemented
8C3×#5063C211yesmaximal, characteristic, complemented
9C3×#5030C211yesmaximal, characteristic, complemented
10C3×#5028C211yesmaximal, characteristic, complemented
11C3×#5028C211yesmaximal, characteristic, complemented
12C3×#5027C211yesmaximal, characteristic
13C3×#5026C211yesmaximal, characteristic, complemented
14C3×C4×#215C211yesmaximal, characteristic, complemented
15C3×#5024C211yesmaximal, characteristic, complemented
16C3×#3371—31nomaximal
17#83691C311yesmaximal, characteristic, direct product factor
18C32×C4⋊Q8—21no—
19C32×C4⋊Q8C2211yescharacteristic
20C32×#125—21no—
21C32×#125—21no—
22C32×#125C2211yescharacteristic
23C32×#125C2211yescharacteristic
24C32×C4×Q8—21no—
25C32×C4×Q8C2211yescharacteristic
26C32×C4×Q8C2211yescharacteristic
27C32×C4×Q8C2211yescharacteristic
28C32×C4×Q8C2211yescharacteristic
29C3×#947—21no—
30C2×C3×#216C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C2×C3×#215C2211yescharacteristic
33C3×#894—21no—
34C3×#894—21no—
35C3×#893—21no—
36C3×#875C2211yescharacteristic
37C3×#875C2211yescharacteristic
38C3×#874C2211yescharacteristic
39C3×C4×D12C2211yescharacteristic
40C3×C4×D12C2211yescharacteristic
41C3×C4×Dic6C2211yescharacteristic
42C3×#835C2211yescharacteristic
43C3×#810C2211yescharacteristic
44C3×#810C2211yescharacteristic
45C3×#810C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic
53C3×#808C2211yescharacteristic
54C3×#807C2211yescharacteristic
55C3×C4⋊(C3⋊C8)C2211yescharacteristic
56C3×C4⋊(C3⋊C8)C2211yescharacteristic
57C3×C4⋊(C3⋊C8)C2211yescharacteristic
58C3×#803C2211yescharacteristic
59C3×#803C2211yescharacteristic
60C3×C4×C3⋊C8C2211yescharacteristic
61C3×#559—31no—
62C3×#557—21no—
63C3×#557D311yescharacteristic, complemented
64C3×#557C2×C311yescharacteristic, complemented
65#5585C2×C311yescharacteristic
66C3×#490—31no—
67C3×#489—31no—
68C3×#488—31no—
69C3×#479—31no—
70C3×#478—31no—
71C3×#476—31no—
72C3×#464—31no—
73C3×#464—31no—
74C3×#460—31no—
75C3×#446—31no—
76C3×#441—31no—
77C3×#440—31no—
78C3×C4×SD16—31no—
79#5089C2×C311yescharacteristic, complemented
80#5084C2×C311yescharacteristic, complemented
81#5068C2×C311yescharacteristic, complemented
82#5067C2×C311yescharacteristic
83#5066C2×C311yescharacteristic, complemented
84#5063C2×C311yescharacteristic, complemented
85#5030C2×C311yescharacteristic, complemented
86#5028C2×C311yescharacteristic, complemented
87#5028C2×C311yescharacteristic, complemented
88#5027C2×C311yescharacteristic
89#5026C2×C311yescharacteristic, complemented
90C4×#215C2×C311yescharacteristic, complemented
91#5024C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8D411yescharacteristic
94C2×C32×Q8C2311yescharacteristic
95C2×C3×D12—21no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×Dic6C2311yescharacteristic
102C32×C4⋊C4—21no—
103C32×C4⋊C4—21no—
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4—21no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4—21no—
110C32×C4⋊C4D411yescharacteristic
111C32×C4⋊C4D411yescharacteristic
112C32×C4⋊C4D411yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C42—21no—
117C32×C42—21no—
118C32×C42—21no—
119C32×C42C2311yescharacteristic
120C32×C42C2311yescharacteristic
121C32×C42C2311yescharacteristic
122C3×#216—22no—
123C3×#215—22no—
124C3×#215—22no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3371—31noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C2×C3×SD16—31no—
142C3×C4⋊Q8—22no—
143C3×C4⋊Q8—21no—
144C3×C4⋊Q8—21no—
145C3×C4⋊Q8—21no—
146C3×C4⋊Q8C2×D311yescharacteristic
147C3×C4⋊Q8C22×C311yescharacteristic
148C3×#127—31no—
149C3×#125—22no—
150C3×#125—22no—
151C3×#125—21no—
152C3×#125—21no—
153C3×#125—21no—
154C3×#125—21no—
155C3×#125—21no—
156C3×#125—21no—
157C3×#125C2×D311yescharacteristic
158C3×#125C2×D311yescharacteristic
159C3×#125C22×C311yescharacteristic
160C3×#125C22×C311yescharacteristic
161C3×#124—31no—
162C3×#124—31no—
163C3×#124—61no—
164C3×#123—61no—
165C3×#123—61no—
166C3×C4×Q8—22no—
167C3×C4×Q8—21no—
168C3×C4×Q8—21no—
169C3×C4×Q8—21no—
170C3×C4×Q8—21no—
171C3×C4×Q8—21no—
172C3×C4×Q8—21no—
173C3×C4×Q8—31no—
174C3×C4×Q8C2×D311yescharacteristic
175C3×C4×Q8C2×D311yescharacteristic
176C3×C4×Q8C2×D311yescharacteristic
177C3×C4×Q8C2×D311yescharacteristic
178C3×C4×Q8C22×C311yescharacteristic
179C3×C4×Q8C22×C311yescharacteristic
180C3×C4×Q8C22×C311yescharacteristic
181C3×C4×Q8C22×C311yescharacteristic
182C3×C4×D4—31no—
183C3×C4×D4—31no—
184C3×C4×D4—61no—
185#947—21no—
186C2×#216C22×C311yescharacteristic
187C2×#215C22×C311yescharacteristic
188C2×#215C22×C311yescharacteristic
189#894—21no—
190#894—21no—
191#893—21no—
192#875C22×C311yescharacteristic
193#875C22×C311yescharacteristic
194#874C22×C311yescharacteristic
195C4×D12C22×C311yescharacteristic
196C4×D12C22×C311yescharacteristic
197C4×Dic6C22×C311yescharacteristic
198C3×#107—31no—
199C3×#106—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#97—31no—
215C3×#97—31no—
216C3×C4×C8—31no—
217#835C22×C311yescharacteristic
218#810C22×C311yescharacteristic
219#810C22×C311yescharacteristic
220#810C22×C311yescharacteristic
221#809C22×C311yescharacteristic
222#809C22×C311yescharacteristic
223#809C22×C311yescharacteristic
224#809C22×C311yescharacteristic
225#809C22×C311yescharacteristic
226#809C22×C311yescharacteristic
227#808C22×C311yescharacteristic
228#808C22×C311yescharacteristic
229#807C22×C311yescharacteristic
230C4⋊(C3⋊C8)C22×C311yescharacteristic
231C4⋊(C3⋊C8)C22×C311yescharacteristic
232C4⋊(C3⋊C8)C22×C311yescharacteristic
233#803C22×C311yescharacteristic
234#803C22×C311yescharacteristic
235C4×C3⋊C8C22×C311yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C32×Q8—21no—
239C32×Q8—41no—
240C32×Q8—42no—
241C32×Q8#4112yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—42no—
260C3×D12—81no—
261C3×C4×D3—81no—
262C3×C4×D3—81no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×C3⋊C8—21no—
266C3×C3⋊C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#559—31no—
270#557C3×D311yescharacteristic, complemented
271#490—31no—
272#489—31no—
273#488—31no—
274#479—31no—
275#478—31no—
276#476—31no—
277#464—31no—
278#464—31no—
279#460—31no—
280#446—31no—
281#441—31no—
282#440—31no—
283C4×SD16—31no—
284C2×C3×Q8—22no—
285C2×C3×Q8—21no—
286C2×C3×Q8—21no—
287C2×C3×Q8—21no—
288C2×C3×Q8—21no—
289C2×C3×Q8—31no—
290C2×C3×Q8#6711yescharacteristic
291C2×C3×Q8C3×D411yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C23×C311yescharacteristic
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C2×D12—21no—
301C2×D12—21no—
302C2×D12C23×C311yescharacteristic
303C2×D12C23×C311yescharacteristic
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×Dic6C23×C311yescharacteristic
307C3×Q16—62no—
308C3×SD16—62no—
309C3×SD16—62no—
310C2×C3×C8—31no—
311C2×C3×C8—31no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C3×C4⋊C4—22no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—22no—
317C3×C4⋊C4—22no—
318C3×C4⋊C4—22no—
319C3×C4⋊C4—22no—
320C3×C4⋊C4—22no—
321C3×C4⋊C4—22no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4#6711yescharacteristic
347C3×C4⋊C4#6711yescharacteristic
348C3×C4⋊C4#6711yescharacteristic
349C3×C4⋊C4C3×D411yescharacteristic
350C3×C4⋊C4C3×D411yescharacteristic
351C3×C4⋊C4C3×D411yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C23×C311yescharacteristic
356C3×C4⋊C4C23×C311yescharacteristic
357C3×C4⋊C4C23×C311yescharacteristic
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—22no—
365C3×C42—22no—
366C3×C42—22no—
367C3×C42—21no—
368C3×C42—21no—
369C3×C42—21no—
370C3×C42—21no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—61no—
377C3×C42C22×D311yescharacteristic
378C3×C42C22×D311yescharacteristic
379C3×C42C22×D311yescharacteristic
380C3×C42C23×C311yescharacteristic
381C3×C42C23×C311yescharacteristic
382C3×C42C23×C311yescharacteristic
383#216—22no—
384#215—22no—
385#215—22no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392C4⋊Dic3C23×C311yescharacteristic
393Dic3⋊C4—21no—
394C4×Dic3—21no—
395C2×C3⋊C8C23×C311yescharacteristic
396C2×C3⋊C8C23×C311yescharacteristic
397C2×C3⋊C8C23×C311yescharacteristic
398C2×C3⋊C8C23×C311yescharacteristic
399C22×C32C22×D411yescharacteristic
400C2×C3×D3—41no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C32×C4—22no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—21no—
410C32×C4—21no—
411C32×C4—21no—
412C32×C4—21no—
413C32×C4—41no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C42−1+411yescharacteristic
418C3×Dic3—41no—
419C3×Dic3—41no—
420C2×Q16—31no—
421C2×SD16—31no—
422C2×SD16—31no—
423C4⋊Q8—21no—
424C4⋊Q8C2×C3×D311yescharacteristic
425#127—31no—
426#125—21no—
427#125—21no—
428#125C2×C3×D311yescharacteristic
429#125C2×C3×D311yescharacteristic
430#124—31no—
431#124—31no—
432#124—61no—
433#123—61no—
434#123—61no—
435C4×Q8—21no—
436C4×Q8—31no—
437C4×Q8C2×C3×D311yescharacteristic
438C4×Q8C2×C3×D311yescharacteristic
439C4×Q8C2×C3×D311yescharacteristic
440C4×Q8C2×C3×D311yescharacteristic
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—61no—
444#107—31no—
445#106—31no—
446#106—31no—
447C4⋊C8—31no—
448C4⋊C8—31no—
449C4⋊C8—31no—
450#103—31no—
451#103—31no—
452#103—31no—
453#103—31no—
454#102—31no—
455#102—31no—
456#102—31no—
457#102—31no—
458#102—31no—
459#102—31no—
460#97—31no—
461#97—31no—
462C4×C8—31no—
463C23×C3—61no—
464C23×C3—61no—
465C22×D3—21no—
466C22×D3—21no—
467C3×Q8—22no—
468C3×Q8—21no—
469C3×Q8—21no—
470C3×Q8—22no—
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—42no—
474C3×Q8—44no—
475C3×Q8—42no—
476C3×Q8—42no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8#23912yes—
480C3×Q8C3×#4112yes—
481C3×D4—61no—
482C3×D4—61no—
483C3×D4—61no—
484C3×D4—61no—
485C3×D4—122no—
486C3×D4—241no—
487C2×C3×C4—22no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—241no—
509C2×C3×C4—241no—
510C2×C3×C4C2×#6711yescharacteristic
511C2×C3×C4C2×#6711yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C2×#6711yescharacteristic
514C2×C3×C4C2×#6711yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C2×C3×D411yescharacteristic
517C2×C3×C4C2×C3×D411yescharacteristic
518C2×C3×C4C2×C3×D411yescharacteristic
519C2×C3×C4C2×C3×D411yescharacteristic
520C2×C3×C4C2×C3×D411yescharacteristic
521C2×C3×C4C2×C3×D411yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C24×C311yescharacteristic
524C2×Dic3—21no—
525C2×Dic3—21no—
526D12—21no—
527D12—21no—
528D12—21no—
529D12—21no—
530D12—42no—
531D12—81no—
532C4×D3—81no—
533C4×D3—81no—
534Dic6—21no—
535Dic6—21no—
536C3×C8—61no—
537C3×C8—61no—
538C3×C8—61no—
539C3×C8—61no—
540C3⋊C8—21no—
541C3⋊C8—21no—
542C3⋊C8—21no—
543C3⋊C8—21no—
544C2×C32#54811yescharacteristic
545C2×C32#57511yescharacteristic
546C2×C32#57711yescharacteristic
547C3×D3—81no—
548C3×D3—81no—
549C2×Q8—21no—
550C2×Q8—31no—
551C2×Q8C3×#6711yescharacteristic
552C2×Q8C22×C3×D311yescharacteristic
553C2×D4—31no—
554C2×D4—31no—
555C2×D4—61no—
556C2×D4—61no—
557C22×C4—61no—
558C22×C4—61no—
559Q16—62no—
560SD16—62no—
561SD16—62no—
562C2×C8—31no—
563C2×C8—31no—
564C2×C8—31no—
565C2×C8—31no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—31no—
575C4⋊C4—61no—
576C4⋊C4C3×#6711yescharacteristic
577C4⋊C4C3×#6711yescharacteristic
578C4⋊C4C3×#6711yescharacteristic
579C4⋊C4C22×C3×D311yescharacteristic
580C4⋊C4C22×C3×D311yescharacteristic
581C4⋊C4C22×C3×D311yescharacteristic
582C22⋊C4—61no—
583C22⋊C4—61no—
584C22⋊C4—61no—
585C22⋊C4—61no—
586C22⋊C4—61no—
587C22⋊C4—61no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—61no—
592C42C22×C3×D311yescharacteristic
593C42C22×C3×D311yescharacteristic
594C42C22×C3×D311yescharacteristic
595C22×C3—21no—
596C22×C3—121no—
597C22×C3—121no—
598C22×C3—121no—
599C22×C3—121no—
600C22×C3—121no—
601C22×C3—121no—
602C22×C3C22×#6711yescharacteristic
603C22×C3C22×C3×D411yescharacteristic
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C3×C4—24no—
611C3×C4—22no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—22no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—22no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—42no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4C2×#23911yescharacteristic
645C3×C4#100711yescharacteristic
646C3×C4C2×C3×#4111yescharacteristic
647C3×C4C3×2−1+411yescharacteristic
648Dic3—41no—
649Dic3—41no—
650C32#337111yescharacteristic, complemented, Sylow
651C23—61no—
652C23—61no—
653Q8—21no—
654Q8—41no—
655Q8—42no—
656Q8—61no—
657Q8—61no—
658Q8C3×#23912yes—
659D4—61no—
660D4—61no—
661D4—61no—
662D4—61no—
663D4—122no—
664D4—241no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—241no—
672C2×C4—241no—
673C2×C4C2×C3×#6711yescharacteristic
674C2×C4C2×C3×#6711yescharacteristic
675C2×C4C2×C3×#6711yescharacteristic
676C2×C4C2×C3×#6711yescharacteristic
677C2×C4C2×C3×#6711yescharacteristic
678C2×C4C2×C3×#6711yescharacteristic
679C2×C4C23×C3×D311yescharacteristic
680C8—61no—
681C8—61no—
682C8—61no—
683C8—61no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—241no—
688C2×C3—241no—
689C2×C3#581711yescharacteristic
690C2×C3#582211yescharacteristic
691C2×C3#583711yescharacteristic
692C2×C3C3×#54811yescharacteristic
693C2×C3C3×#57511yescharacteristic
694C2×C3C3×#57711yescharacteristic
695D3—81no—
696D3—81no—
697C22—121no—
698C22—121no—
699C22—121no—
700C22—121no—
701C22—121no—
702C22—121no—
703C22C22×C3×#6711yescharacteristic
704C4—22no—
705C4—21no—
706C4—21no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—21no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—121no—
715C4—121no—
716C4C2×C3×#23911yescharacteristic
717C4C3×#100711yescharacteristic
718C3—21no—
719C3#8369111yescharacteristic, direct product factor
720C3C3×#337111yescharacteristic, complemented
721C2—241no—
722C2—241no—
723C2C3×#581711yescharacteristic
724C2C3×#582211yescharacteristic
725C2C3×#583711yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#557C2
socleC22×C32C22×D4
prime radicalC3×#874C22
hypercenterC3×#557D3
hypocenterC3C3×#3371
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×Q8 ◁ C3×#557

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C32×#557C2semidirect
3. C3×#5089C2semidirect
4. C3×#5084C2semidirect
5. C3×#5068C2semidirect
7. C3×#5066C2semidirect
8. C3×#5063C2semidirect
9. C3×#5030C2semidirect
10. C3×#5028C2semidirect
11. C3×#5028C2semidirect
13. C3×#5026C2semidirect
14. C3×C4×#215C2semidirect
15. C3×#5024C2semidirect
17. #83691C3direct (N × H)
63. C3×#557D3semidirect
64. C3×#557C2×C3semidirect
79. #5089C2×C3semidirect
80. #5084C2×C3semidirect
81. #5068C2×C3semidirect
83. #5066C2×C3semidirect
84. #5063C2×C3semidirect
85. #5030C2×C3semidirect
86. #5028C2×C3semidirect
87. #5028C2×C3semidirect
89. #5026C2×C3semidirect
90. C4×#215C2×C3semidirect
91. #5024C2×C3semidirect
270. #557C3×D3semidirect
650. C32#3371semidirect
719. C3#83691direct (N × H)
720. C3C3×#3371semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×#5572
C3×#55852
C3×#50892
C3×#50842
C3×#50682
C3×#50672
C3×#50662
C3×#50632
C3×#50302
C3×#50282
C3×#50272
C3×#50262
C3×C4×#2152
C3×#50242
C3×#33713
#836913